Adaptive Volatility: A Robustness Test Using Global Risk Parity

In the last post we introduced the concept of using adaptive volatility in order to have a flexible lookback as a function of market conditions. We used the R-squared of price as a proxy for the strength of the trend in the underlying market in order to vary the half-life in an exponential moving average framework. The transition function used an exponential formula to translate to a smoothing constant. There are many reasons why this approach might be desirable from a regime or state dependent volatility framework, to improving the  mitigation of tail risk by being more responsive to market feedback loops as mentioned in this article from Alpha Architect. In the latter case, by shortening the volatility lookback when the market seems to be forming a bubble in either direction (as measured by trend measures such as the Hurst Exponent or R-squared) we can more rapidly adjust volatility to changes in the market conditions.

In order to test the robustness of the adaptive volatility measure we decided to follow the approach of forming risk parity portfolios which was inspired by this article by Newfound Research. Our simple Global Risk Parity portfolio uses five major asset classes: Domestic Equities (VTI), Commodities (DBC), International Equity (EFA), Bonds (IEF), and Real Estate (ICF). The choice of VTI was deliberate since we already did the first test using SPY. VTI contains the full spectrum of domestic equities including large, mid and small cap whereas SPY is strictly large cap. We created simple risk parity portfolios (position size is equivalent to 1/vol scaled to the sum of inverse vol across assets) with weekly rebalancing and a 1-day delay in execution. For realized volatility portfolios we ran each individually using various parameters including  20-day, 60-day, 252-day and all history. To test adaptive volatility we ran 27 different portfolios that varied the maximum smoothing constant and the r-squared lookback. The smoothing constant was varied between .1,.5 and .9 and the R-squared lookback was varied using 10,12,15,20,25,30,40,50 and 60 days. We chose to keep the multiplier (-10 in the original post) the same since it was a proxy for the longest possible lookback (all history) by design. The testing period was from 1995 to present and we used extensions with indices for the ETFs when necessary to go back in time. In the graph below we chart the return versus risk for each portfolio.

 

We used a line to separate the performance of the realized volatility portfolios to better illustrate the superiority in performance of the adaptive volatility portfolios. All parameter combinations outperformed the realized volatility portfolios on a return basis. In terms of risk-adjusted return or sharpe ratio, the realized volatility portfolios fell on the 0%, 3.3%, 13.3% and 33% percentile in the distribution of all portfolios- in other words nearly all the adaptive portfolios also outperformed on a risk-adjusted basis. Was there any systematic advantage to using certain parameters for the adaptive volatility portfolios? As it turns out the maximum smoothing constant was less important than the choice of R-squared. We stated in the previous post that shorter r-squared parameters on average were more desirable than long parameters as long as they weren’t too short so as to avoid capturing noise. Shorter lookbacks should allow the adaptive volatility to more rapidly adjust to current market conditions and therefore reduce drawdowns and improve returns. It turns out that this pattern is validated when we average across smoothing constant values (hold them constant) and look at the return relative to maximum drawdown (MAR)  as a function of R-squared lookback.

 

 

 

 

 

 

 

 

 

 

 

 

Clearly the shorter-term R-squared values improved the return relative to maximum drawdown. While not shown, the drawdowns were much lower and drove this effect, while the returns showed a more modest improvement. The drawback to shorter lookbacks is increased turnover, which can be mitigated by longer rebalancing windows or through improved smoothing measures or rules to mitigate allocation changes without materially affecting results. Another alternative is to average all possible r-squared and smoothing constant portfolios with a tilt toward shorter r-squared parameters to have a good balance between responsiveness and smoothness while mitigating the risk of a poor parameter choice.

In conclusion, this simple robustness test appears to show that adaptive volatility is relatively robust and may have practical value as a substitute or complement to realized volatility. We will do some single stock tests in order to further investigate this effect and possibly compare to traditional forecasting methods such as GARCH.  Additional exploration on this concept could be done to vary the transition formula or choice of trend indicator. Finally, it may be valuable to test these methods in a more formal volatility forecasting model rather than using just a backtest, and calibrate the parameters according to which are most effective every day.

 

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